Abstract

A facile method is presented for the fabrication of microlenses at the facet of fused silica capillaries and microstructured fibers. After submersion in hydrogen fluoride solution water is pumped slowly through the center hole of the capillary microchannel to create an etchant gradient extending from the capillary axis. The desired axicon angle is generated by adjusting the etching time and/or concentration of the etchant. Similarly, flow- assisted HF etching of a custom microstructured fiber containing nine microchannels produces nine individual microlenses simultaneously at the fiber facet, where each microaxicon lens shows a similar focusing pattern. A theoretical model of the flow-assisted etching process is used to determine the axicon angle and post angle. Also, a simple ray-based model was applied to characterize the focusing properties of the microaxicons in good agreement with experimental observations.

© 2016 Optical Society of America

1. Introduction

Bessel beams [1] exhibit a tight focal spot in the transverse plane, and a focal volume that is elongated along the optical axis compared to that produced by a spherical lens. Due to their non-diffracting, “self-healing” nature, Bessel beams are employed in a wide variety of applications including non-linear optics [2], lithography [3], microfabrication [4], atom-trapping [5], and optical tweezers [6] among others. Bessel beams can be created using optical components such as an annular aperture located at the focal plane of a lens, spatial light modulation, computer generated holograms or more simply through the use of axicon lenses. First reported in 1954 by McLeod et al. [7], axicons generate Bessel beams from collimated beams of light using a cone-shaped lens. Since then, axicon lenses have been used in a wide range of devices and applications. The fabrication of axicon lenses on the facet of multimode fibers (i.e. microaxicons or microaxicon lenses) has been carried out using fiber polishing [8], and focused ion beam technology [9] however most fabrication strategies have focused on wet-chemical etching with hydrofluoric acid, HF [10, 11], using either the Turner [12] or tube-etching [13] methods.

The Turner method involves etching a fiber at the meniscus between an organic layer and hydrofluoric acid with its protective polymer coating removed [12]. The process produces a tapered structure due to the decreasing height of the meniscus as the fiber diameter is reduced [6]. During tube-etching, the fiber’s acrylate coating is not removed and acts as a protective shell to maintain the integrity of the outer portion of the fiber [13]. The etching process proceeds in the hollow cylinder formed by the coating as the glass is gradually removed by etching. After the etching is complete, the protective coating is removed chemically, e.g. using hot concentrated sulfuric acid, or by mechanical stripping [13]. Eisenstein and Vitello initially reported the use of wet-chemical etching to produce an axicon lens on the end of a single-mode optical fiber and showed that the height of conical lenses protruding from the core of a fiber could be controlled by adjusting the composition and temperature of the etchant solution [10]. The resulting lensed fiber improved the coupling of single-mode injection lasers and single-mode fibers. Later, Eah et al. utilized wet-chemical etching to produce a microaxicon on the facet of a commercially available single-mode fiber [11]. Mohanty et al. used differential etching and a modified tube-etching method to fabricate an axicon with cone angles varying from 30° to 60° on the tip of an optical fiber. The microaxicon lenses were utilized to trap low-index microscopic objects [14]. Kuchmizhak et al. recently reported the fabrication of high quality microaxicons on the end-face of optical fibers using the tube-etching method [15]. The authors correlated fiber composition and microaxicon formation. A lengthy (up to seven hours per fiber) but effective tube-etching method involved placing the fiber in a solution of concentrated HF (40%) for several hours. Ion-beam milling was then applied to remove a portion of the tapered end, and the fiber was immersed again in an aqueous solution of HF (10%). In this way microaxicons with excellent axial symmetry and highly tunable angles were produced. The authors also showed the Bessel-like beam profiles of the microaxicons, however the lengthy, multi-step, fabrication somewhat limits its scale-up.

In this paper, we fabricate single microaxicon lenses on the end facets of conventional silica capillaries. These capillaries may be used for optical trapping where the particle is introduced on-axis by delivery through the same capillary that provides the focusing of the co-propagated light beam. Such devices also allow for optical excitation and possible evaporation of a sample at the end of the capillary waveguide. A model is provided to describe the formation of an etchant gradient. The consequent differential etch rates are used to control the axicon angle. The same protocol was also used to fabricate microaxicons at the end of nine borosilicate-doped capillaries that are contained in a custom-designed multichannel microstructured optical fiber. Etching gradients that are created by slowly flowing water into the etching solution permit the rapid and simultaneous fabrication of several fiber microlenses in less than 20 minutes.

2. Experimental

2.1. Fiber fabrication

The custom microstructured fiber (MSF) was fabricated at the Centre for Optics, Photonics and Lasers (COPL, Québec City, Canada). A detailed description of the fiber fabrication is presented in previous work by Fu I [16]. Briefly, a set of borosilicate- and silicate rods are stacked in the desired arrangement around a large borosilicate core and silica capillaries are inserted within the structure to produce a preform. The capillaries are arranged equidistantly in a radial pattern. The preform is then drawn into a fiber with desired dimensions (MSF Ø360 μm, silica core Ø50 μm, and capillary bore Ø8 μm) by adjusting the drawing speed. An optical micrograph and scanning electron micrograph of the microstructured fiber are shown in Fig. 1.

 

Fig. 1 (A) Optical micrograph and (B) scanning electron micrograph of the custom-designed microstructured fiber utilized in this study. The dark shaded regions of the fiber in image (A) correspond to regions of borosilicate (9 mol%) glass while the light shaded regions correspond to fused-silica. Scale bar in (B) is 100 µm

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2.2. Microlens fabrication

Prior to etching a capillary (e.g. Polymicro Ø360 µm, bore Ø10 µm), the protective polyimide jacket was removed from the fiber using a wire stripper (Stripall TWC-1, Teledyne Impulse, San Diego, CA, USA). The protective acrylate jacket of other capillaries could also be removed chemically using dichloromethane. Following the removal of the jacket the bare capillary was cleaved using a precision fiber cleaver (LDC-400, Vytran, Morganville, NJ, USA). When the cleave quality is deemed acceptable (assessed by optical microscopy), the capillary was connected to a syringe filled with degassed, deionized water and placed on a syringe pump (Harvard Apparatus Pump 11 Plus, Holliston, MA, USA). The syringe pump was used to control the flow rate of deionized water passing through the channels of the capillaries. When the capillaries are contained in a microstructured fiber bundle, the flow through each channel must be similar and consistent in order to ensure that all microlenses are identical. The flow speed and was monitored using a USB microscope (Veho VMS-004D) prior to submersing the capillaries in the etchant. After allowing sufficient time (1-5 minutes) for flow equilibration through the channels, the end of the capillary/fiber was submersed in a solution of concentrated hydrofluoric acid (48 wt%) such that the capillary did not contact the edges of the container and was perpendicular to the surface of the HF solution. The capillary was etched at 22 ± 1°C with a constant flow (~50 nL/min for a capillary and ~80 nL/min for MSF) for different durations depending on the desired etch profile.

2.3. Optical characterization of microlenses

We inspected the focusing pattern created by the axicon lenses using an optical microscope whose optical axis is co-aligned with the capillary axis. The axicon lenses were examined by increasing the distance between the microscope’s objective lens and the axicon base in well-controlled increments [10]. While the axicon end of the capillary is mounted on the translation stage of the microscope, light from a 532 nm laser diode is coupled into the free end of the capillary. Images are taken at regular distance intervals (5 µm) and compiled into cross sections using ImageJ software (US National Institutes of Health). A schematic drawing of the experimental setup for image acquisition is shown in Fig. 2.

 

Fig. 2 Schematic diagram of experimental set-up for imaging the emission patterns of microlenses on the facet of capillaries and microstructured fibers.

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The microlenses formed on the silica portions of the MSF were similarly characterized (at Université Laval) using a CMOS camera that was mounted on a single-axis translation stage in order to facilitate movement through the focal range of the microlenses without moving the fiber and compromising the light coupling. The camera was moved from the face of the fiber in 10 µm increments and images were taken at each interval. These fibers were also characterized using an optical microscope and a 980 nm source (otherwise analogous to the capillary microlenses) wherein the z movement of the objective was digitally measured with 0.5 µm resolution.

2.4. Scanning electron microscopy

Scanning electron micrographs (SEM) were taken (FEI Quanta 650 FEG ESEM) to characterize the microlens shape and the overall fiber profile. SEM and optical imaging was performed before and after microlens optical measurements to ensure no structural changes had occurred during the measurement process. SEM analysis was also performed to measure the angle of the microlenses. All SEM images where obtained under low vacuum conditions without the presence of a conductive coating.

3. Ray optics model

A cone-shaped tip at the end of a multimode optical waveguide is expected to retain some of the inherent properties of a conventional axicon lens. The main difference is due to the multimode nature of the capillary or fiber. Instead of a plane wave interacting with the conical surface, the light rays in a multimode waveguide are exiting the fiber at a range of angles given by the numerical aperture of the fiber. Modelling of the emission pattern therefore requires sampling light rays at all possible refraction angles. Of relevance to the current study is the intensity distribution in the medium outside the cone-terminated waveguide as well as inside the axicon lens itself.

A variety of methods are suited to modelling this intensity distribution. Considering that all dimensions are large compared to the wavelength of the light we used a simple ray tracing approach. Also, instead of performing a Monte-Carlo type approach to determine the irradiated volume elements for each ray of light, we inverted the problem and determine for each volume element in the sample space the number of surface elements on the axicon lens that contribute rays to its irradiation. The approach is fast and exact as well as physically intuitive. Since the system has cylindrical symmetry, it is sufficient to solve the two-dimensional problem. The three-dimensional intensity distribution can be readily obtained from an Abel transformation [17, 18].

In our calculations the following assumptions were used:

  • 1. The wave nature of light was neglected; effects due to coherence were ignored.
  • 2. Only a single refraction or reflection was included in the calculations; this had the consequence that rays that were internally reflected inside the axicon lens were not followed once they were emitted by the lens.
  • 3. Reflections at sub-critical angles (Fresnel reflections) were ignored. This also had the consequence that refracted light always carried the initial intensity.
  • 4. The multimode fiber was assumed to be perfectly filled, i.e. all internal reflection angles in the range permitted by the numerical aperture were assumed to be equally likely.
  • 5. Absorption and scattering was ignored.
  • 6. The center hole of the capillary was ignored.

We closely followed an approach that has been described before for the calculation of multimode fiber lenses [17–19]. In this method the intensity of each pixel {x,y} is calculated by adding light rays that emanate from the two finely incremented lines that form the profile of the axicon lens [Fig. 3].

 

Fig. 3 Schematic drawing of rays incident on the surface of the axicon microlens. (A) shows two rays that are contributing to the intensity increase at the optical axis, (B) shows two rays that contribute to the ring pattern observable at large cone angles. (C) Light ray showing internal reflection at the inner axicon surface.

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For light that is focussed outside the axicon lens in a medium with refractive index n0, the intensity at point {x,y} is incremented by one unit if the angle ϕuxy falls between the two limiting angles β1 and β2. In addition, the intensity is incremented by one more unit if the angle ϕdxy falls between -β1 and -β2. These angles are β1 = ϕs1 - γ and β2 = ϕs1 + γ. From Snell’s law

sinϕs1,2=ncoren0sinϕf1,2
where ncore and n0 are the refractive indices of the fiber core and the surrounding medium, respectively. The two limiting incidence angles at the inner surface of the axicon lens are ϕf1 = π/2 - θc + γ and ϕf2 = π/2 - θc - γ . The critical incidence angle inside the multimode fiber is governed by the refractive index of the cladding, nclad:

θc=sin1(ncladncore)

Given the refractive indices n0, nclad and ncore, as well as the cone angle, γ, of the axicon lens it is straightforward to determine the range of angles, β1 and β2, that can be irradiated from each point on the surface of the axicon lens. These angles are then compared to the two angles defining the point in the sample space that is under consideration, i.e.

ϕxyu=tan1(yyACLxxACL)ϕxyd=tan1(y+yACLxxACL)

Here, 0 < yACL < R and xACL = (R - yACL) tan(γ), with R being the radius of the core of the multimode fiber. When β1 < ϕuxy < β2 the intensity is incremented due to irradiation from the upper half of the axicon lens and when −β1 > ϕdxy > −β2 the intensity is incremented due to irradiation from the lower half.

A similar calculation was performed to model the intensity of the light inside the axicon lens [Fig. 3(c)]. For large cone angles, γ, the guided light in the multimode fiber is likely to undergo total internal reflection on the inside of the axicon lens, thereby creating a region of increased light intensity below the tip of the lens. A point inside the axicon lens will be irradiated by reflected light only if the angle ϕx,y < θc - γ and ϕx,y < θACL - π/2. The critical angle for guided light in the fiber, θc, is given by (2), whereas that for total internal reflection at the axicon surface is

θACL=sin1(n0ncore)
The angle ϕxy is more complicated to determine but can be concisely described as
ϕxy=cos1(a+bc4ab)a=(xACLx)2+(yACLy)2b=(xACLxp)2+(yACLyp)2c=(xpx)2+(ypy)2,
where the coordinates of the axicon tip are xp = R sinγ and yp = 0. The intensity at {x,y} is then calculated as above, i.e. by incrementing yACL between 0 and R and determining xACL = (R - yACL) tan(γ) as well as all three angles ϕx,y, θc and θACL as described above. The intensity is incremented by one unit, if ϕx,y is smaller than both angles θc and θACL.

Example results are shown in Fig. 4 for axicon lenses with cone angles between 0 and 50 degrees. Note that these are 2-dimensional calculations and an image representing the intensity distribution as seen by an observer requires an Abel transformation as in [17].

 

Fig. 4 Two-dimensional representations of the calculated intensity distribution inside and outside axicon lenses with different cone angles. Angles in the range of about 10-40 degrees produce a bright focal region in front of the axicon lens. At larger cone angles the light is predominantly reflected inside the cone and only then leaves the cone. These rays are not shown in the figure.

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In their modelling of axicon lenses obtained by tube-etching Kuchmizhak et al. used the finite difference time domain method to obtain the optical properties of their micro-axicons [15]. These FDTD calculations are preferred for single mode fibers and coherent light sources, as they will correctly reproduce interference patterns. In our case of a fully filled, multimode waveguide having hundreds or even thousands of modes, the above raytracing method provides a simple, fast and accurate solution to an otherwise cumbersome problem.

4. Results and discussion

4.1. Microlens fabrication via wet-chemical etching

While fused-silica capillaries are primarily designed for fluidics applications and not designed to guide light, they offer structural and chemical properties similar to optical fibers. Without the presence of preventative water flow, wet-chemical etching of a glass capillary or “holey” microstructured fiber would proceed both, from the outer walls and etching inward as well as the etchant diffusing into the channel and etching outward. This results in the rapid expansion of the channel to form a much larger bore, and eventually in the destruction of the capillary walls. To control the etching process, we introduce water-flow at a rate comparable to the diffusion rate of etchant into the channel, which ensures that the etching proceeds only from the outer walls of the capillary. The constant flow of water through the capillary (into the etchant solution) also dilutes the etchant. More importantly the water flow introduced an etchant concentration gradient extending radially from the center axis of the waveguide. A single tapered fused-silica cone, or “micronozzle”, is then formed from the originally flat facet of the capillary [Figs. 5(b) and 5(e)]. We show below that this cone acts as a microaxicon lens.

 

Fig. 5 (A) Modelled emission pattern for 15° axicon lens, (B) Optical micrograph of 15° lens in front of a Ø320 μm capillary, (C) experimental emission pattern of 15° lens. (D)-(F) are the analogous images for a 35° lens.

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The length of the protruding micronozzles and their cone angle can be adjusted through the etch time, etchant concentration, and/or the flow rate of water during the etching procedure. For example, longer etch times or higher HF concentration results in longer nozzle protrusion. Figure 5(b) shows a microaxicon with a cone angle of approximately 15° produced after etching for 10 min and Fig. 5(e) shows a microaxicon with an approximately 35° cone angle which is formed after 20 minutes of etching in HF solution. The water flow rate was kept constant. The shape of the axicon lens reflects presumably the concentration gradient of the HF solution.

Etching of the custom “holey” MSF results in several microaxicons which were formed at the end of each of the nine channels. As opposed to the single capillaries, the MSF contains two different types of glass. As for the single capillary, the microaxicon is fabricated from fused silica, which in this case is embedded in borosilicate glass. The borosilicate glass is etched much faster by HF solution and, as it is removed, it exposed the sidewalls of the embedded fused-silica capillary. The process is readily modelled using simple rate equations.

Our model describes the etching kinetics and the geometry of the final structure based on a few simple assumptions. We assume that the material removal rate depends linearly on the constant concentration of the etchant, [HF], and a rate constant, k, that is different for the borosilicate glass (k1) and undoped silicate glass (k2).

dxdt=ki[HF]X

The HF concentration is furthermore assumed to vary linearly between the inner rim of the water filled capillary, [HF]D, and the outer border of the silicate capillary, [HF]C. (see the profile on top of Fig. 6(c)) The axicon angle is then determined as

γ=tan1(ΔxCΔxDR)=tan1(k2tR([HF]D[HF]C))
where we usedΔxC,D=k2t[HF]C,Dby integration of (6). The axicon angle therefore increases as a function of etch time, as observed. The “post angle”, α, can similarly be obtained as described earlier by Kotsas et al. [20] using the integral of (6)

 

Fig. 6 Scanning electron micrographs of the micronozzles (microlenses) produced by etching the custom microstructured fiber for (A) 12 minutes and (B) for 17 minutes with ~80 nL/min water flow through the centre holes. Inset images show the entire fiber profile. All scale bars are 50 µm. (C) Schematic diagram of microlens (micronozzle) formation as the etching procedure occurs. (1) and (2) correspond to borosilicate and fused-silica compositions, respectively, while R0 is the distance from the channel wall to the borosilicate boundary (i.e. the base width) and R is the width of the top portion of the microlens.

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ΔxB=k2[HF]B(ttA)

Since the sidewall is only etched after the borosilicate (1) has been removed, we need to consider the removal rate of the borosilicate glass, since this will determine the lower integration limit. This consideration yields

tA=ΔxAk1[HF]A
and insertion into (8) gives:
ΔxB=k2[HF]Btk2k1[HF]B[HF]AΔxA.
Setting [HF]A = [HF]B for simplicity, the line describing the post wall at any time, τ, is therefore:
xA=k1[HF]Bτk1k2xB
and, as was pointed out previously [20], the post angle is given by the angle between xA and xB
α=cos1(k1k2)
It is expected to be largely independent of etching time. The radius of the axicon lenses,
R=R0ΔxBcos(α)
can be calculated using (8), (9) and (12) to give

R=R0k1[HF]Bt+ΔxA

In the SEM micrographs [Fig. 6(a) and 6(b)] the two cone angles are clearly discernable. The axicon angle, γ is dependent on the concentration gradient and increases with time according to Eq. (7). It changes from 30° to 36° degrees as the etching time is increased from 10 to 20 minutes. The post angle α only depends on the ratio of the etch rate constants of borosilicate glass and fused silica according to Eq. (12). As expected, it remains approximately constant between 10 minutes etch time (72°) and 20 minutes (70°) [Figs. 6(a) and 6(b)].

4.2. Optical characteristics of microaxicons

4.2.1. Microaxicons on capillaries

The ability of the microaxicons to focus light was evaluated by following the protocol explained in Section 2.3. Images were captured at 5 µm intervals from the base of the microlens extending to 400 µm from the tip of the axicon. These images were processed to give a 2D intensity cross section containing the capillary axis. Two examples are displayed in Figs. 5(c) and 5(f). The tight but elongated focal regions extending from the tip of the axicon lenses confirm that the etched capillaries indeed produce Bessel-type beams. It is also obvious that the longer etch time leads to a larger axicon angle and consequently to a tighter focus near the tip of the microaxicon. These experimental data show a 2D cross section of the focusing characteristics, similar to the result of the calculation shown in Figs. 5(a) and 5(d). Yet, there are differences between these figures. By design the experimental microscope images show light in the focal plane of the microscope but also a blurred background of unfocussed light. Figures 5(c) and 5(f) therefore show a constant presence of light over the entire travel distance which diverges (visible especially in Fig. 5(f)) due to blurring, but not to beam divergence. Nevertheless, the experimental images confirm that for the 35° cone angle we observe a focal region near the top of the cone at about 170 μm, which agrees very well with the theoretical prediction. At a cone angle of 15° the focal region is found to be 290 μm, whereas our simulation predicts it to be at about 240 μm. The agreement is better than what might be expected, especially considering that the shape of the tip is not an ideal cone [Figs. 5(b) and 5(e)].

The center hole in the capillaries is expected to have only a small effect on the optical properties of the fiber microaxicon lenses. The hole diameter is only 10 μm whereas the capillary diameter is 320 μm. Given that the ratio of the cross sectional areas is about 1:1000, it may therefore not be too surprising that the contributions of rays exiting the hole is not observed.

4.2.2. MSF microlenses

The fused silica portion of the microstructured waveguide has a higher refractive index of ncore = 1.464 at 655 nm compared to the borosilicate glass (nclad = 1.461). The silica portions of the MSF therefore behave like cladded multimode fiber waveguides. The microaxicons on the MSF are then expected to have similar focusing characteristics compared to the microaxicons formed on the fused silica capillaries. We found that the MSF showed good light guiding properties within the silica regions of the fiber. Similar to the capillary-microlenses, the focusing behavior of two fibers each having nine microaxicons with nearly identical etch profiles were characterized to validate the formation of axicon lenses. Again, the focusing properties of the microlenses were obtained following the protocol outlined in Section 2.4. It was observed that each of the nine microaxicons at the facets of the two fibers had a tight focal point with very little extension in the transverse plane. We also found that the focal points are strongly dependent on the etch profile, i.e. on the HF concentration and submersion duration. The focal points were found by immobilizing the fiber and coupling light into the free end of the fiber while the microscope objective was translated away from the microaxicons. The region of the smallest and brightest spots was identified in five replicate experiments for two different MSF microaxicon profiles (shown in Fig. 6). By averaging the 9 focal points in each fiber and the 5 trials we obtained focal lengths of 40.8 ± 1.6 µm for the shallow-angle microaxicons in Fig. 6(a) and 15.6 ± 1.1 µm for the larger axicon angles of Fig. 6(b). Figure 7 shows an example of how the focal length was determined using laser-coupled optical microscopy.

 

Fig. 7 Optical micrographs of (A) lens tips in focus and (B) from ~40 µm away from lens tip showing the focal point of a shallow etched MSF. These images show 3 of the 9 microlenses on the facet of the MSF of Fig. 6(A). The scale bars are 50 µm in both images.

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5. Conclusions

Microaxicon lenses can be readily fabricated at the end of capillaries using a slow water flow through the capillary holes while the capillary is submersed in an etching solution. The process can be readily understood with a simple kinetic model that involves a concentration gradient extending radially from the center of the capillary as well as the respective etch rates of the glasses. The experimentally obtained focusing characteristics are not greatly influenced by the presence of the center hole and can be modelled using ray tracing with incoherent ballistic photons. By adjusting the etchant concentration and/or etching time the axicon angle can be controlled, which gives good control over the focusing properties of the capillary microaxicons. We note that simultaneous fabrication of high quality axicons at the end of the same holey MSF would be nearly impossible by mechanical (polishing) methods and would be considerably more complicated if charged particle milling was employed.

We anticipate that axicon microlenses similar to those produced in this work find applications as injector nozzles for mass spectrometry and even in multiple particle trapping.

Acknowledgments

The authors thank Jeff Crouse for technical assistance. The authors acknowledge financial support from the Natural Sciences and Engineering Research Council (NSERC) of Canada. KB thanks the Collaborative Research and Training Experience Program (CREATE) of NSERC for supporting his visit to Université Laval.

References and links

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2. T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 71(1), 209 (1993). [CrossRef]  

3. M. Erdelyi, Z. L. Horvath, G. Szabo, Z. Bor, F. K. Tittel, J. R. Cavallaro, and M. C. Smayling, “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15(2), 287–292 (1997). [CrossRef]  

4. A. Marcinkevicius, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Application of Bessel beams for microfabrication of dielectrics by femtosecond laser,” Jpn. J. Appl. Phys. 2(40), L1197–L1199 (2001). [CrossRef]  

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8. T. Grosjean, S. S. Saleh, M. A. Suarez, I. A. Ibrahim, V. Piquerey, D. Charraut, and P. Sandoz, “Fiber microaxicons fabricated by a polishing technique for the generation of Bessel-like beams,” Appl. Opt. 46(33), 8061–8067 (2007). [CrossRef]   [PubMed]  

9. S. Cabrini, C. Liberale, D. Cojoc, A. Carpentiero, M. Prasciolu, S. Mora, V. Degiorgio, F. De Angelis, and E. Di Fabrizio, “Axicon lens on optical fiber forming optical tweezers, made by focused ion beam milling,” Microelectron. Eng. 83(4-9), 804–807 (2006). [CrossRef]  

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11. S. K. Eah, W. Jhe, and Y. Arakawa, “Nearly diffraction-limited focusing of a fiber axicon microlens,” Rev. Sci. Instrum. 74(11), 4969–4971 (2003). [CrossRef]  

12. P. Hoffmann, B. Dutoit, and R. P. Salathe, “Comparison of mechanically drawn and protection layer chemically etched optical fiber tips,” Ultramicroscopy 61(1-4), 165–170 (1995). [CrossRef]  

13. R. Stöckle, C. Fokas, V. Deckert, R. Zenobi, B. Sick, B. Hecht, and U. P. Wild, “High-quality near-field optical probes by tube etching,” Appl. Phys. Lett. 75(2), 160–162 (1999). [CrossRef]  

14. S. K. Mohanty, K. S. Mohanty, and M. W. Berns, “Organization of microscale objects using a microfabricated optical fiber,” Opt. Lett. 33(18), 2155–2157 (2008). [CrossRef]   [PubMed]  

15. A. Kuchmizhak, S. Gurbatov, A. Nepomniaschii, O. Vitrik, and Y. Kulchin, “High-quality fiber microaxicons fabricated by a modified chemical etching method for laser focusing and generation of Bessel-like beams,” Appl. Opt. 53(5), 937–943 (2014). [CrossRef]   [PubMed]  

16. Y. Fu, S. Morency, K. Bachus, D. Simon, T. Hutama, G. T. T. Gibson, Y. Messaddeq, and R. D. Oleschuk, “A microstructured fiber with defined borosilicate regions to produce a radial micronozzle array for nanoelectrospray ionization,” Sci. Rep.-UK 6(2016).

17. K. Bescherer, D. Munzke, O. Reich, and H.-P. Loock, “Fabrication and modeling of multimode fiber lenses,” Appl. Opt. 52(4), B40–B45 (2013). [CrossRef]   [PubMed]  

18. D. Munzke, J. Saunders, H. Omrani, O. Reich, and H.-P. Loock, “Modeling of fiber-optic fluorescence probes for strongly absorbing samples,” Appl. Opt. 51(26), 6343–6351 (2012). [CrossRef]   [PubMed]  

19. G. He and F. W. Cuomo, “A light-intensity function suitable for multimode fiberoptic sensors,” J. Lightwave Technol. 9(4), 545–551 (1991). [CrossRef]  

20. A. Kotsas, H. Ghafourishiraz, and T. S. M. Maclean, “Microlens fabrication on single-mode fibers for efficient coupling from laser-diodes,” Opt. Quantum Electron. 23(3), 367–378 (1991). [CrossRef]  

References

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  1. J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
    [Crossref] [PubMed]
  2. T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 71(1), 209 (1993).
    [Crossref]
  3. M. Erdelyi, Z. L. Horvath, G. Szabo, Z. Bor, F. K. Tittel, J. R. Cavallaro, and M. C. Smayling, “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15(2), 287–292 (1997).
    [Crossref]
  4. A. Marcinkevicius, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Application of Bessel beams for microfabrication of dielectrics by femtosecond laser,” Jpn. J. Appl. Phys. 2(40), L1197–L1199 (2001).
    [Crossref]
  5. Y. Song, D. Milam, and W. T. Hill, “Long, narrow all-light atom guide,” Opt. Lett. 24(24), 1805–1807 (1999).
    [Crossref] [PubMed]
  6. R. S. R. Ribeiro, O. Soppera, A. G. Oliva, A. Guerreiro, and P. A. S. Jorge, “New trends on optical fiber tweezers,” J. Lightwave Technol. 33(16), 3394–3405 (2015).
    [Crossref]
  7. J. H. McLeod, “The axicon - a new type of optical element,” J. Opt. Soc. Am. 44(8), 592–597 (1954).
    [Crossref]
  8. T. Grosjean, S. S. Saleh, M. A. Suarez, I. A. Ibrahim, V. Piquerey, D. Charraut, and P. Sandoz, “Fiber microaxicons fabricated by a polishing technique for the generation of Bessel-like beams,” Appl. Opt. 46(33), 8061–8067 (2007).
    [Crossref] [PubMed]
  9. S. Cabrini, C. Liberale, D. Cojoc, A. Carpentiero, M. Prasciolu, S. Mora, V. Degiorgio, F. De Angelis, and E. Di Fabrizio, “Axicon lens on optical fiber forming optical tweezers, made by focused ion beam milling,” Microelectron. Eng. 83(4-9), 804–807 (2006).
    [Crossref]
  10. G. Eisenstein and D. Vitello, “Chemically etched conical microlenses for coupling single-mode lasers into single-mode fibers,” Appl. Opt. 21(19), 3470–3474 (1982).
    [Crossref] [PubMed]
  11. S. K. Eah, W. Jhe, and Y. Arakawa, “Nearly diffraction-limited focusing of a fiber axicon microlens,” Rev. Sci. Instrum. 74(11), 4969–4971 (2003).
    [Crossref]
  12. P. Hoffmann, B. Dutoit, and R. P. Salathe, “Comparison of mechanically drawn and protection layer chemically etched optical fiber tips,” Ultramicroscopy 61(1-4), 165–170 (1995).
    [Crossref]
  13. R. Stöckle, C. Fokas, V. Deckert, R. Zenobi, B. Sick, B. Hecht, and U. P. Wild, “High-quality near-field optical probes by tube etching,” Appl. Phys. Lett. 75(2), 160–162 (1999).
    [Crossref]
  14. S. K. Mohanty, K. S. Mohanty, and M. W. Berns, “Organization of microscale objects using a microfabricated optical fiber,” Opt. Lett. 33(18), 2155–2157 (2008).
    [Crossref] [PubMed]
  15. A. Kuchmizhak, S. Gurbatov, A. Nepomniaschii, O. Vitrik, and Y. Kulchin, “High-quality fiber microaxicons fabricated by a modified chemical etching method for laser focusing and generation of Bessel-like beams,” Appl. Opt. 53(5), 937–943 (2014).
    [Crossref] [PubMed]
  16. Y. Fu, S. Morency, K. Bachus, D. Simon, T. Hutama, G. T. T. Gibson, Y. Messaddeq, and R. D. Oleschuk, “A microstructured fiber with defined borosilicate regions to produce a radial micronozzle array for nanoelectrospray ionization,” Sci. Rep.-UK 6(2016).
  17. K. Bescherer, D. Munzke, O. Reich, and H.-P. Loock, “Fabrication and modeling of multimode fiber lenses,” Appl. Opt. 52(4), B40–B45 (2013).
    [Crossref] [PubMed]
  18. D. Munzke, J. Saunders, H. Omrani, O. Reich, and H.-P. Loock, “Modeling of fiber-optic fluorescence probes for strongly absorbing samples,” Appl. Opt. 51(26), 6343–6351 (2012).
    [Crossref] [PubMed]
  19. G. He and F. W. Cuomo, “A light-intensity function suitable for multimode fiberoptic sensors,” J. Lightwave Technol. 9(4), 545–551 (1991).
    [Crossref]
  20. A. Kotsas, H. Ghafourishiraz, and T. S. M. Maclean, “Microlens fabrication on single-mode fibers for efficient coupling from laser-diodes,” Opt. Quantum Electron. 23(3), 367–378 (1991).
    [Crossref]

2015 (1)

2014 (1)

2013 (1)

2012 (1)

2008 (1)

2007 (1)

2006 (1)

S. Cabrini, C. Liberale, D. Cojoc, A. Carpentiero, M. Prasciolu, S. Mora, V. Degiorgio, F. De Angelis, and E. Di Fabrizio, “Axicon lens on optical fiber forming optical tweezers, made by focused ion beam milling,” Microelectron. Eng. 83(4-9), 804–807 (2006).
[Crossref]

2003 (1)

S. K. Eah, W. Jhe, and Y. Arakawa, “Nearly diffraction-limited focusing of a fiber axicon microlens,” Rev. Sci. Instrum. 74(11), 4969–4971 (2003).
[Crossref]

2001 (1)

A. Marcinkevicius, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Application of Bessel beams for microfabrication of dielectrics by femtosecond laser,” Jpn. J. Appl. Phys. 2(40), L1197–L1199 (2001).
[Crossref]

1999 (2)

Y. Song, D. Milam, and W. T. Hill, “Long, narrow all-light atom guide,” Opt. Lett. 24(24), 1805–1807 (1999).
[Crossref] [PubMed]

R. Stöckle, C. Fokas, V. Deckert, R. Zenobi, B. Sick, B. Hecht, and U. P. Wild, “High-quality near-field optical probes by tube etching,” Appl. Phys. Lett. 75(2), 160–162 (1999).
[Crossref]

1997 (1)

M. Erdelyi, Z. L. Horvath, G. Szabo, Z. Bor, F. K. Tittel, J. R. Cavallaro, and M. C. Smayling, “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15(2), 287–292 (1997).
[Crossref]

1995 (1)

P. Hoffmann, B. Dutoit, and R. P. Salathe, “Comparison of mechanically drawn and protection layer chemically etched optical fiber tips,” Ultramicroscopy 61(1-4), 165–170 (1995).
[Crossref]

1993 (1)

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 71(1), 209 (1993).
[Crossref]

1991 (2)

G. He and F. W. Cuomo, “A light-intensity function suitable for multimode fiberoptic sensors,” J. Lightwave Technol. 9(4), 545–551 (1991).
[Crossref]

A. Kotsas, H. Ghafourishiraz, and T. S. M. Maclean, “Microlens fabrication on single-mode fibers for efficient coupling from laser-diodes,” Opt. Quantum Electron. 23(3), 367–378 (1991).
[Crossref]

1987 (1)

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

1982 (1)

1954 (1)

Arakawa, Y.

S. K. Eah, W. Jhe, and Y. Arakawa, “Nearly diffraction-limited focusing of a fiber axicon microlens,” Rev. Sci. Instrum. 74(11), 4969–4971 (2003).
[Crossref]

Berns, M. W.

Bescherer, K.

Bor, Z.

M. Erdelyi, Z. L. Horvath, G. Szabo, Z. Bor, F. K. Tittel, J. R. Cavallaro, and M. C. Smayling, “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15(2), 287–292 (1997).
[Crossref]

Cabrini, S.

S. Cabrini, C. Liberale, D. Cojoc, A. Carpentiero, M. Prasciolu, S. Mora, V. Degiorgio, F. De Angelis, and E. Di Fabrizio, “Axicon lens on optical fiber forming optical tweezers, made by focused ion beam milling,” Microelectron. Eng. 83(4-9), 804–807 (2006).
[Crossref]

Carpentiero, A.

S. Cabrini, C. Liberale, D. Cojoc, A. Carpentiero, M. Prasciolu, S. Mora, V. Degiorgio, F. De Angelis, and E. Di Fabrizio, “Axicon lens on optical fiber forming optical tweezers, made by focused ion beam milling,” Microelectron. Eng. 83(4-9), 804–807 (2006).
[Crossref]

Cavallaro, J. R.

M. Erdelyi, Z. L. Horvath, G. Szabo, Z. Bor, F. K. Tittel, J. R. Cavallaro, and M. C. Smayling, “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15(2), 287–292 (1997).
[Crossref]

Charraut, D.

Cojoc, D.

S. Cabrini, C. Liberale, D. Cojoc, A. Carpentiero, M. Prasciolu, S. Mora, V. Degiorgio, F. De Angelis, and E. Di Fabrizio, “Axicon lens on optical fiber forming optical tweezers, made by focused ion beam milling,” Microelectron. Eng. 83(4-9), 804–807 (2006).
[Crossref]

Cuomo, F. W.

G. He and F. W. Cuomo, “A light-intensity function suitable for multimode fiberoptic sensors,” J. Lightwave Technol. 9(4), 545–551 (1991).
[Crossref]

De Angelis, F.

S. Cabrini, C. Liberale, D. Cojoc, A. Carpentiero, M. Prasciolu, S. Mora, V. Degiorgio, F. De Angelis, and E. Di Fabrizio, “Axicon lens on optical fiber forming optical tweezers, made by focused ion beam milling,” Microelectron. Eng. 83(4-9), 804–807 (2006).
[Crossref]

Deckert, V.

R. Stöckle, C. Fokas, V. Deckert, R. Zenobi, B. Sick, B. Hecht, and U. P. Wild, “High-quality near-field optical probes by tube etching,” Appl. Phys. Lett. 75(2), 160–162 (1999).
[Crossref]

Degiorgio, V.

S. Cabrini, C. Liberale, D. Cojoc, A. Carpentiero, M. Prasciolu, S. Mora, V. Degiorgio, F. De Angelis, and E. Di Fabrizio, “Axicon lens on optical fiber forming optical tweezers, made by focused ion beam milling,” Microelectron. Eng. 83(4-9), 804–807 (2006).
[Crossref]

Di Fabrizio, E.

S. Cabrini, C. Liberale, D. Cojoc, A. Carpentiero, M. Prasciolu, S. Mora, V. Degiorgio, F. De Angelis, and E. Di Fabrizio, “Axicon lens on optical fiber forming optical tweezers, made by focused ion beam milling,” Microelectron. Eng. 83(4-9), 804–807 (2006).
[Crossref]

Durnin, J.

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Dutoit, B.

P. Hoffmann, B. Dutoit, and R. P. Salathe, “Comparison of mechanically drawn and protection layer chemically etched optical fiber tips,” Ultramicroscopy 61(1-4), 165–170 (1995).
[Crossref]

Eah, S. K.

S. K. Eah, W. Jhe, and Y. Arakawa, “Nearly diffraction-limited focusing of a fiber axicon microlens,” Rev. Sci. Instrum. 74(11), 4969–4971 (2003).
[Crossref]

Eberly, J. H.

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Eisenstein, G.

Erdelyi, M.

M. Erdelyi, Z. L. Horvath, G. Szabo, Z. Bor, F. K. Tittel, J. R. Cavallaro, and M. C. Smayling, “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15(2), 287–292 (1997).
[Crossref]

Fokas, C.

R. Stöckle, C. Fokas, V. Deckert, R. Zenobi, B. Sick, B. Hecht, and U. P. Wild, “High-quality near-field optical probes by tube etching,” Appl. Phys. Lett. 75(2), 160–162 (1999).
[Crossref]

Ghafourishiraz, H.

A. Kotsas, H. Ghafourishiraz, and T. S. M. Maclean, “Microlens fabrication on single-mode fibers for efficient coupling from laser-diodes,” Opt. Quantum Electron. 23(3), 367–378 (1991).
[Crossref]

Grosjean, T.

Guerreiro, A.

Gurbatov, S.

He, G.

G. He and F. W. Cuomo, “A light-intensity function suitable for multimode fiberoptic sensors,” J. Lightwave Technol. 9(4), 545–551 (1991).
[Crossref]

Hecht, B.

R. Stöckle, C. Fokas, V. Deckert, R. Zenobi, B. Sick, B. Hecht, and U. P. Wild, “High-quality near-field optical probes by tube etching,” Appl. Phys. Lett. 75(2), 160–162 (1999).
[Crossref]

Herminghaus, S.

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 71(1), 209 (1993).
[Crossref]

Hill, W. T.

Hoffmann, P.

P. Hoffmann, B. Dutoit, and R. P. Salathe, “Comparison of mechanically drawn and protection layer chemically etched optical fiber tips,” Ultramicroscopy 61(1-4), 165–170 (1995).
[Crossref]

Horvath, Z. L.

M. Erdelyi, Z. L. Horvath, G. Szabo, Z. Bor, F. K. Tittel, J. R. Cavallaro, and M. C. Smayling, “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15(2), 287–292 (1997).
[Crossref]

Ibrahim, I. A.

Jhe, W.

S. K. Eah, W. Jhe, and Y. Arakawa, “Nearly diffraction-limited focusing of a fiber axicon microlens,” Rev. Sci. Instrum. 74(11), 4969–4971 (2003).
[Crossref]

Jorge, P. A. S.

Juodkazis, S.

A. Marcinkevicius, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Application of Bessel beams for microfabrication of dielectrics by femtosecond laser,” Jpn. J. Appl. Phys. 2(40), L1197–L1199 (2001).
[Crossref]

Kotsas, A.

A. Kotsas, H. Ghafourishiraz, and T. S. M. Maclean, “Microlens fabrication on single-mode fibers for efficient coupling from laser-diodes,” Opt. Quantum Electron. 23(3), 367–378 (1991).
[Crossref]

Kuchmizhak, A.

Kulchin, Y.

Liberale, C.

S. Cabrini, C. Liberale, D. Cojoc, A. Carpentiero, M. Prasciolu, S. Mora, V. Degiorgio, F. De Angelis, and E. Di Fabrizio, “Axicon lens on optical fiber forming optical tweezers, made by focused ion beam milling,” Microelectron. Eng. 83(4-9), 804–807 (2006).
[Crossref]

Loock, H.-P.

Maclean, T. S. M.

A. Kotsas, H. Ghafourishiraz, and T. S. M. Maclean, “Microlens fabrication on single-mode fibers for efficient coupling from laser-diodes,” Opt. Quantum Electron. 23(3), 367–378 (1991).
[Crossref]

Marcinkevicius, A.

A. Marcinkevicius, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Application of Bessel beams for microfabrication of dielectrics by femtosecond laser,” Jpn. J. Appl. Phys. 2(40), L1197–L1199 (2001).
[Crossref]

Matsuo, S.

A. Marcinkevicius, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Application of Bessel beams for microfabrication of dielectrics by femtosecond laser,” Jpn. J. Appl. Phys. 2(40), L1197–L1199 (2001).
[Crossref]

McLeod, J. H.

Miceli, J.

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Milam, D.

Misawa, H.

A. Marcinkevicius, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Application of Bessel beams for microfabrication of dielectrics by femtosecond laser,” Jpn. J. Appl. Phys. 2(40), L1197–L1199 (2001).
[Crossref]

Mizeikis, V.

A. Marcinkevicius, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Application of Bessel beams for microfabrication of dielectrics by femtosecond laser,” Jpn. J. Appl. Phys. 2(40), L1197–L1199 (2001).
[Crossref]

Mohanty, K. S.

Mohanty, S. K.

Mora, S.

S. Cabrini, C. Liberale, D. Cojoc, A. Carpentiero, M. Prasciolu, S. Mora, V. Degiorgio, F. De Angelis, and E. Di Fabrizio, “Axicon lens on optical fiber forming optical tweezers, made by focused ion beam milling,” Microelectron. Eng. 83(4-9), 804–807 (2006).
[Crossref]

Munzke, D.

Nepomniaschii, A.

Oliva, A. G.

Omrani, H.

Piquerey, V.

Prasciolu, M.

S. Cabrini, C. Liberale, D. Cojoc, A. Carpentiero, M. Prasciolu, S. Mora, V. Degiorgio, F. De Angelis, and E. Di Fabrizio, “Axicon lens on optical fiber forming optical tweezers, made by focused ion beam milling,” Microelectron. Eng. 83(4-9), 804–807 (2006).
[Crossref]

Reich, O.

Ribeiro, R. S. R.

Salathe, R. P.

P. Hoffmann, B. Dutoit, and R. P. Salathe, “Comparison of mechanically drawn and protection layer chemically etched optical fiber tips,” Ultramicroscopy 61(1-4), 165–170 (1995).
[Crossref]

Saleh, S. S.

Sandoz, P.

Saunders, J.

Sick, B.

R. Stöckle, C. Fokas, V. Deckert, R. Zenobi, B. Sick, B. Hecht, and U. P. Wild, “High-quality near-field optical probes by tube etching,” Appl. Phys. Lett. 75(2), 160–162 (1999).
[Crossref]

Smayling, M. C.

M. Erdelyi, Z. L. Horvath, G. Szabo, Z. Bor, F. K. Tittel, J. R. Cavallaro, and M. C. Smayling, “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15(2), 287–292 (1997).
[Crossref]

Song, Y.

Soppera, O.

Stöckle, R.

R. Stöckle, C. Fokas, V. Deckert, R. Zenobi, B. Sick, B. Hecht, and U. P. Wild, “High-quality near-field optical probes by tube etching,” Appl. Phys. Lett. 75(2), 160–162 (1999).
[Crossref]

Suarez, M. A.

Szabo, G.

M. Erdelyi, Z. L. Horvath, G. Szabo, Z. Bor, F. K. Tittel, J. R. Cavallaro, and M. C. Smayling, “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15(2), 287–292 (1997).
[Crossref]

Tittel, F. K.

M. Erdelyi, Z. L. Horvath, G. Szabo, Z. Bor, F. K. Tittel, J. R. Cavallaro, and M. C. Smayling, “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15(2), 287–292 (1997).
[Crossref]

Vitello, D.

Vitrik, O.

Wild, U. P.

R. Stöckle, C. Fokas, V. Deckert, R. Zenobi, B. Sick, B. Hecht, and U. P. Wild, “High-quality near-field optical probes by tube etching,” Appl. Phys. Lett. 75(2), 160–162 (1999).
[Crossref]

Wulle, T.

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 71(1), 209 (1993).
[Crossref]

Zenobi, R.

R. Stöckle, C. Fokas, V. Deckert, R. Zenobi, B. Sick, B. Hecht, and U. P. Wild, “High-quality near-field optical probes by tube etching,” Appl. Phys. Lett. 75(2), 160–162 (1999).
[Crossref]

Appl. Opt. (5)

Appl. Phys. Lett. (1)

R. Stöckle, C. Fokas, V. Deckert, R. Zenobi, B. Sick, B. Hecht, and U. P. Wild, “High-quality near-field optical probes by tube etching,” Appl. Phys. Lett. 75(2), 160–162 (1999).
[Crossref]

J. Lightwave Technol. (2)

G. He and F. W. Cuomo, “A light-intensity function suitable for multimode fiberoptic sensors,” J. Lightwave Technol. 9(4), 545–551 (1991).
[Crossref]

R. S. R. Ribeiro, O. Soppera, A. G. Oliva, A. Guerreiro, and P. A. S. Jorge, “New trends on optical fiber tweezers,” J. Lightwave Technol. 33(16), 3394–3405 (2015).
[Crossref]

J. Opt. Soc. Am. (1)

J. Vac. Sci. Technol. B (1)

M. Erdelyi, Z. L. Horvath, G. Szabo, Z. Bor, F. K. Tittel, J. R. Cavallaro, and M. C. Smayling, “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15(2), 287–292 (1997).
[Crossref]

Jpn. J. Appl. Phys. (1)

A. Marcinkevicius, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Application of Bessel beams for microfabrication of dielectrics by femtosecond laser,” Jpn. J. Appl. Phys. 2(40), L1197–L1199 (2001).
[Crossref]

Microelectron. Eng. (1)

S. Cabrini, C. Liberale, D. Cojoc, A. Carpentiero, M. Prasciolu, S. Mora, V. Degiorgio, F. De Angelis, and E. Di Fabrizio, “Axicon lens on optical fiber forming optical tweezers, made by focused ion beam milling,” Microelectron. Eng. 83(4-9), 804–807 (2006).
[Crossref]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

A. Kotsas, H. Ghafourishiraz, and T. S. M. Maclean, “Microlens fabrication on single-mode fibers for efficient coupling from laser-diodes,” Opt. Quantum Electron. 23(3), 367–378 (1991).
[Crossref]

Phys. Rev. Lett. (2)

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 71(1), 209 (1993).
[Crossref]

Rev. Sci. Instrum. (1)

S. K. Eah, W. Jhe, and Y. Arakawa, “Nearly diffraction-limited focusing of a fiber axicon microlens,” Rev. Sci. Instrum. 74(11), 4969–4971 (2003).
[Crossref]

Ultramicroscopy (1)

P. Hoffmann, B. Dutoit, and R. P. Salathe, “Comparison of mechanically drawn and protection layer chemically etched optical fiber tips,” Ultramicroscopy 61(1-4), 165–170 (1995).
[Crossref]

Other (1)

Y. Fu, S. Morency, K. Bachus, D. Simon, T. Hutama, G. T. T. Gibson, Y. Messaddeq, and R. D. Oleschuk, “A microstructured fiber with defined borosilicate regions to produce a radial micronozzle array for nanoelectrospray ionization,” Sci. Rep.-UK 6(2016).

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Figures (7)

Fig. 1
Fig. 1 (A) Optical micrograph and (B) scanning electron micrograph of the custom-designed microstructured fiber utilized in this study. The dark shaded regions of the fiber in image (A) correspond to regions of borosilicate (9 mol%) glass while the light shaded regions correspond to fused-silica. Scale bar in (B) is 100 µm
Fig. 2
Fig. 2 Schematic diagram of experimental set-up for imaging the emission patterns of microlenses on the facet of capillaries and microstructured fibers.
Fig. 3
Fig. 3 Schematic drawing of rays incident on the surface of the axicon microlens. (A) shows two rays that are contributing to the intensity increase at the optical axis, (B) shows two rays that contribute to the ring pattern observable at large cone angles. (C) Light ray showing internal reflection at the inner axicon surface.
Fig. 4
Fig. 4 Two-dimensional representations of the calculated intensity distribution inside and outside axicon lenses with different cone angles. Angles in the range of about 10-40 degrees produce a bright focal region in front of the axicon lens. At larger cone angles the light is predominantly reflected inside the cone and only then leaves the cone. These rays are not shown in the figure.
Fig. 5
Fig. 5 (A) Modelled emission pattern for 15° axicon lens, (B) Optical micrograph of 15° lens in front of a Ø320 μm capillary, (C) experimental emission pattern of 15° lens. (D)-(F) are the analogous images for a 35° lens.
Fig. 6
Fig. 6 Scanning electron micrographs of the micronozzles (microlenses) produced by etching the custom microstructured fiber for (A) 12 minutes and (B) for 17 minutes with ~80 nL/min water flow through the centre holes. Inset images show the entire fiber profile. All scale bars are 50 µm. (C) Schematic diagram of microlens (micronozzle) formation as the etching procedure occurs. (1) and (2) correspond to borosilicate and fused-silica compositions, respectively, while R0 is the distance from the channel wall to the borosilicate boundary (i.e. the base width) and R is the width of the top portion of the microlens.
Fig. 7
Fig. 7 Optical micrographs of (A) lens tips in focus and (B) from ~40 µm away from lens tip showing the focal point of a shallow etched MSF. These images show 3 of the 9 microlenses on the facet of the MSF of Fig. 6(A). The scale bars are 50 µm in both images.

Equations (14)

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sin ϕ s1,2 = n core n 0 sin ϕ f1,2
θ c = sin 1 ( n clad n core )
ϕ xy u = tan 1 ( y y ACL x x ACL ) ϕ xy d = tan 1 ( y+ y ACL x x ACL )
θ ACL = sin 1 ( n 0 n core )
ϕ xy = cos 1 ( a+bc 4ab ) a= ( x ACL x ) 2 + ( y ACL y ) 2 b= ( x ACL x p ) 2 + ( y ACL y p ) 2 c= ( x p x ) 2 + ( y p y ) 2 ,
dx dt = k i [HF] X
γ= tan 1 ( Δ x C Δ x D R )= tan 1 ( k 2 t R ( [ HF ] D [ HF ] C ) )
Δ x B = k 2 [ HF ] B ( t t A )
t A = Δ x A k 1 [ HF ] A
Δ x B = k 2 [ HF ] B t k 2 k 1 [ HF ] B [ HF ] A Δ x A .
x A = k 1 [ HF ] B τ k 1 k 2 x B
α= cos 1 ( k 1 k 2 )
R= R 0 Δ x B cos( α )
R= R 0 k 1 [ HF ] B t+Δ x A

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